Exponents Of Real Numbers — Maths STD 9 — Question
Maharashtra BoardEnglish MediumSTD 9MathsExponents Of Real Numbers1 Mark
MCQ
$(256)^{0.16} \times(256)^{0.09}$
✓
$4$
B
$16$
C
$64$
D
$265.25$
✓
Answer
Correct option: A.
$4$
We have to find the value of $(256)^{0.16} \times (256)^{0.09}$.
So,
By using law of rational exponents
$a^m \times a^n= a^{m+n}$ we get
$(265)^{0.16} \times (256)^{0.09} = (256)^{0.16} \times (256)^{0.09}$
$= (256)^{0.16+0.09}$
$=256^{0.25}$
$=256^{\frac{25}{100}}$
$(256)^{0.16}\times(256)^{0.09 }=2^{8\times\frac{25}{100}}$
$=2^{8\times\frac{25}{100}}$
$=2^{8\times\frac{1}{4}}$
$=2^{8\times\frac{1}{4}}$
$=4$
The value of $(256)^{0.16} \times (256)^{0.09}$ is $4$
Hence the correct choice is $a.$
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